Optimal control of switched nonlinear systems with application to chemical processes

The switched system contains several subsystems with different dynamics, of which the optimal control is to establish a switching law that determines the sequence of subsystems, the switching time, and the control input to minimise the cost function. Without imposing additional constraints, such as the number of switches and the sequence of subsystems, this paper investigates the optimal control of the switched nonlinear system and its application to chemical processes. The HJB equation for the switched system is constructed, and the switching law is given accordingly. Galerkin's spectral method is introduced for approximating unknown optimal value functions and optimal input. A numerical continuous stirred tank reactor example demonstrates the effectiveness and the system performance improvement of the proposed method. To our knowledge, this paper is the first attempt to investigate the optimal control of switched CSTR systems.